Semirings, automata, languages
Semirings, automata, languages
Solution of the Sylvester matrix equation AXBT + CXDT = E
ACM Transactions on Mathematical Software (TOMS)
The Kronecker product in approximation and fast transform generation
The Kronecker product in approximation and fast transform generation
The ubiquitous Kronecker product
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. III: linear algebra
Automata, Languages, and Machines
Automata, Languages, and Machines
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Semiring frameworks and algorithms for shortest-distance problems
Journal of Automata, Languages and Combinatorics
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Classes of kernels for machine learning: a statistics perspective
The Journal of Machine Learning Research
State of the art of graph-based data mining
ACM SIGKDD Explorations Newsletter
Cyclic pattern kernels for predictive graph mining
Proceedings of the tenth ACM SIGKDD international conference on Knowledge discovery and data mining
Extensions of marginalized graph kernels
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Rational Kernels: Theory and Algorithms
The Journal of Machine Learning Research
SIAM Journal on Matrix Analysis and Applications
Shortest-Path Kernels on Graphs
ICDM '05 Proceedings of the Fifth IEEE International Conference on Data Mining
2005 Speical Issue: Graph kernels for chemical informatics
Neural Networks - Special issue on neural networks and kernel methods for structured domains
Structure and evolution of online social networks
Proceedings of the 12th ACM SIGKDD international conference on Knowledge discovery and data mining
Proceedings of the 25th international conference on Machine learning
Tree Covering within a Graph Kernel Framework for Shape Classification
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Indexing of 3d models based on graph of surfacic regions
Proceedings of the ACM workshop on 3D object retrieval
Geometry aware local kernels for object recognition
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part I
Learning graph prototypes for shape recognition
Computer Vision and Image Understanding
High order structural matching using dominant cluster analysis
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Graph characterization via backtrackless paths
SIMBAD'11 Proceedings of the First international conference on Similarity-based pattern recognition
A nonparametric classification method based on K-associated graphs
Information Sciences: an International Journal
Inexact graph matching based on kernels for object retrieval in image databases
Image and Vision Computing
Weisfeiler-Lehman Graph Kernels
The Journal of Machine Learning Research
Graph embedding in vector spaces by node attribute statistics
Pattern Recognition
Using graph-based program characterization for predictive modeling
Proceedings of the Tenth International Symposium on Code Generation and Optimization
A structural cluster kernel for learning on graphs
Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining
Effective graph classification based on topological and label attributes
Statistical Analysis and Data Mining
Combining information extraction, deductive reasoning and machine learning for relation prediction
ESWC'12 Proceedings of the 9th international conference on The Semantic Web: research and applications
Redundant dictionary spaces as a general concept for the analysis of non-vectorial data
ICDM'12 Proceedings of the 12th Industrial conference on Advances in Data Mining: applications and theoretical aspects
Two new graphs kernels in chemoinformatics
Pattern Recognition Letters
Similarity measures for sequential data
Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery
Pattern Recognition Letters
Fast top-k similarity queries via matrix compression
Proceedings of the 21st ACM international conference on Information and knowledge management
Efficient graph kernels by randomization
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
Scalable relation prediction exploiting both intrarelational correlation and contextual information
ECML PKDD'12 Proceedings of the 2012 European conference on Machine Learning and Knowledge Discovery in Databases - Volume Part I
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
Transforming graph data for statistical relational learning
Journal of Artificial Intelligence Research
Fuzzy Sets and Systems
Entity disambiguation in anonymized graphs using graph kernels
Proceedings of the 22nd ACM international conference on Conference on information & knowledge management
Geometric tree kernels: classification of COPD from airway tree geometry
IPMI'13 Proceedings of the 23rd international conference on Information Processing in Medical Imaging
Subtree selection in kernels for graph classification
International Journal of Data Mining and Bioinformatics
Type Extension Trees for feature construction and learning in relational domains
Artificial Intelligence
A lossy counting based approach for learning on streams of graphs on a budget
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
Learning kernels on extended Reeb graphs for 3d shape classification and retrieval
3DOR '13 Proceedings of the Sixth Eurographics Workshop on 3D Object Retrieval
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We present a unified framework to study graph kernels, special cases of which include the random walk (Gärtner et al., 2003; Borgwardt et al., 2005) and marginalized (Kashima et al., 2003, 2004; Mahét al., 2004) graph kernels. Through reduction to a Sylvester equation we improve the time complexity of kernel computation between unlabeled graphs with n vertices from O(n6) to O(n3). We find a spectral decomposition approach even more efficient when computing entire kernel matrices. For labeled graphs we develop conjugate gradient and fixed-point methods that take O(dn3) time per iteration, where d is the size of the label set. By extending the necessary linear algebra to Reproducing Kernel Hilbert Spaces (RKHS) we obtain the same result for d-dimensional edge kernels, and O(n4) in the infinite-dimensional case; on sparse graphs these algorithms only take O(n2) time per iteration in all cases. Experiments on graphs from bioinformatics and other application domains show that these techniques can speed up computation of the kernel by an order of magnitude or more. We also show that certain rational kernels (Cortes et al., 2002, 2003, 2004) when specialized to graphs reduce to our random walk graph kernel. Finally, we relate our framework to R-convolution kernels (Haussler, 1999) and provide a kernel that is close to the optimal assignment kernel of kernel of Fröhlich et al. (2006) yet provably positive semi-definite.